CFA Level I · CFA Level I Exam · Curve-Based and Empirical Fixed-Income Risk Measures
A bond has an analytical duration of 7.0. Historical data show its yield changes by 0.60% for every 1.00% change in the government benchmark yield (a yield beta of 0.60). The bond's empirical duration relative to the benchmark yield is closest to:
Empirical duration is about 4.2. It equals analytical duration of 7.0 multiplied by the yield beta of 0.60, because the bond's yield moves only 0.60% for each 1.00% benchmark move. Dividing by the beta, or ignoring it, gives wrong results.
- A4.2Correct
- B7.0
- C11.7
Explanation
Empirical duration is approximately analytical duration times the yield beta: 7.0 × 0.60 = 4.2. Choosing 7.0 ignores the beta. Choosing 11.7 divides by the beta (7.0/0.60), which inverts the relationship.
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